(CNN) -- The clock is ticking, and Republicans in the Texas Senate can't do much to stop it as they face a midnight deadline in their effort to pass new abortion legislation that would be among the most restrictive in the nation.

Democrats are promising a filibuster Tuesday to eat up the remaining hours of the 30-day special session

"The reality is: If we're not able to sustain the filibuster ... it's a foregone conclusion, the bills will pass," Sen. Royce West, a Dallas Democrat, told CNN affiliate KXAN.

And while the Republicans hold a majority in the Senate, they don't appear to have the votes to thwart the plan.

The legislation, which has already passed the Texas House, would ban most abortions after 20 weeks of pregnancy and impose stricter standards on abortion clinics and the doctors who work at them.

The goal, supporters say, is to protect women's health.

"It's trying to bring up the quality of the standard of the facility for which those procedures are performed," Republican Sen. Donna Campbell told affiliate KEYE.

Critics say the legislation would result in most of the abortion clinics in the state being shut down.

Should the legislation pass, Republican Gov. Rick Perry, who called the special session, has promised to sign it.

"In Texas, we value all life, and we've worked to cultivate a culture that supports the birth of every child," Perry said. "We have an obligation to protect unborn children, and to hold those who peddle these abortions to standards that would minimize the death, disease and pain they cause."